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~\vspace{8cm}
\begin{center}
    \textbf{\Large Arcata Brackish Marsh Cap Project - Individual Writing Component}
    {\bf\\ Jordan Pierce \\}
    E492 October 13, 2008
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\section{Introduction}
The Arcata marsh waste water treatment system was originally a proof
of concept marsh system developed in the seventies, which later was
expanded to be Arcata's waste water treatment plant.  The system was
redesigned in the eighties to accommodate a population of 19,056
(from the design book). Since then, population increases and
seasonal rainfall has put numerous heavy loadings on the system
causing incompliance of the discharge permit. Currently, the system
has three oxidation ponds (which reduce BOD), and four treatment
marshes, which reduce TSS.  After exiting the treatment marshes, the
waste water is mixed with water from the enhancement marshes then
sent into the chlorine contact basin.  After chlorination, the water
some of the water (about 1.5 MGD) is sent into the enhancement
marshes, and the rest is discharged into the bay.\\
In order to help reduce incompliances of the discharge permit, and
to only chlorinate once, a brackish marsh in being installed that
will further treat the water and allow the system to better handle
the peak loads.  The brackish marsh will have a tide gate to allow
saltwater mixing and discharge.  The tide gate is designed by Leo
Kuntz of Nehalem Marine and includes a float operated pet door to
allow fish passage and a more continuous mixing.  The Fall 2008
Capstone team is modeling the water routing through the marsh to
help marsh operators know how to prepare for expected peak loads and
to determine the feasibility of running the marsh in several
different configurations.
\section{Literature Review}
\subsection{Tide Gates}
Tide gates have been used for many years to drain estuaries and
marshes, either for land use or to control water breeding insects
such as mosquitoes \cite{Giannico2005}.  Tide gates allow draining
of wetlands into estuaries and bays but prevent the back flow of
brackish water. Tide gates keep the water level within a dike near
the low tide level, and allow tidal wetlands to be dried for
development \cite{Charland1998} Tide gates are single or double
hinged flaps placed at the downstream ends of culverts. Tide gates
can only open in one direction, thus allowing only a unidirectional
flow of water (except in tide gates with pet doors). Tide gates open
during ebb tides, as the upstream head overcomes the downstream head
and the gates weight and friction. Some tide gates have pet doors
which allow for tidal
mixing and fish passage.\\
Determining the elevation of the invert is of special import in tide
gate designs.  If placed too high, the gate might not open at all
during some low tide events, as shown by \cite{Giannico2005} in a
study of tide gates in Coons Bay, Oregon. This can affect water
quality. Also if placed too high, fish passage can be severely
restricted as the tidal cycle will be below the invert during most
of the tidal cycle.\\ Tide gates are designed to receive little or
no maintenance and must be able to withstand floating debris and
strong currents \cite{Charland1998}.
\subsubsection{Types of Tide Gates}
Traditionally tide gates are top hinged, square or round gates that
are made of cast iron or wood \cite{Giannico2005}.  Round gates are
made of cast iron whereas square gates are made of either cast iron
or wood. Cast iron gates can be very heavy, weighing more than 750
pounds \cite{Giannico2005}, which limits how much they open.  This
in turn limits fish passage.  Cast iron gates can last more than 20
years and generally do not need much maintenance.  Wooden gates can
be less heavy, but over time the logs become waterlogged and less
buoyant. Other light materials (such as aluminum, fiberglass, and
PVC) have
been used but are weaker.\\
Side hinged tide gates require little differential head to open, and
open wider than top hinged gates, allowing for better fish passage.
However, side hinged gates are more expensive to install as the
hinges must be slightly off axis so the gate will return to the
closed position under its own forces.  However, these gates are
still fully closed during most of the flood cycle and still present
a significant fish barrier.\\
To help mitigate fish passage and water quality concerns, pet doors
have been developed for many tide gates.  The idea is that pet doors
open very easily and widely for fish passage, but still prevent much
back flow.  All tide gates aforementioned open and close only as a
function of the head difference upstream and downstream of the gate.
Leo Kuntz of Nehalem Marine has developed a gate which remains open
while the upstream pond is below some reference point.  A buoy on
the pond side is linked to a control mechanism that either closes
the gate or allows it to open.  Leo Kuntz has a patent on this
design, called a Muted Tidal Regulator (MTR).  The MTR was designed
specifically to allow tidal mixing upstream for water quality and
fish passage, but prevent upstream water elevations from exceeding
some datum (MTR patent).  The first installment of an MTR tide gate
was in Humboldt Bay, California in the winter of 2004-2005
\cite{Giannico2005}.  The ability of the MTR to allow more tidal
mixing over traditional tide gate designs helps to mitigate many of
the adverse effects of tide gates, and greatly increases fish
passage, fish
usage, and water quality \cite{Porior}\\

\subsubsection{Tide Gate Modeling}
A paper by \cite{Porior} gave a flow model through a pet door.  Two
conditions were analyzed- when the pet door was completely submerged
on the tidal side, and when it was only partially submerged.  In the
first case, the pet door was modeled as an orifice, with the
equation
\begin{equation}
Q=C_dA(2gH)^{0.5}
\end{equation}
where
\begin{align*}
C_d&=0.61\\
L&=\mbox{length (feet)}\\
H&=\mbox{head difference.}
\end{align*}
In the case where the pet door is only partially submerged, the flow
was modeled as a weir with the equation
\begin{equation}
Q=C_dLH^{3/2}
\end{equation}
where
\begin{align*}
C_d&=3.09\\
L&=\mbox{length (feet)}\\
H&=\mbox{head difference.}
\end{align*}
These equations were used to calculate flow and thus velocity in the
culvert to determine if fish could pass upstream.\\
Another paper, by \cite{Litrico2005} describes a hydraulic model for
an automatic control gate, a Begemann gate.  The type of tide gate
modeled was a square, a top hinged, weighted flap were weights were
added to help keep the gate closed.  To model the tide gates,
\cite{Litrico2005} first found the closing moment of the gate, which
is calculated by multiplying the weight of the gate and
counterweight by the distance from the pivot to the gate.  The force
of the water on the gate is hydrostatic when the gate is closed;
however, when the gate opens, the force is assumed to be hydrostatic
and friction forces are assumed negligible.  The angle of opening
($\delta_w$) is calculated from the force of the water.  When
$\delta_w$ is small, \cite{Litrico2005} modeled the flow as an
orifice with the equation
\begin{equation}
Q(h_0)=C_dUB_g\sqrt{2gh_0}
\end{equation}
where
\begin{align*}
C_d&=\mbox{Discharge coefficiet, varies linearly from 0.7 to 1.4}\\
U&=\mbox{The distance between the point of contact of the gate and weir}\\
B_g&=\mbox{Width of the gate}\\
g&=\mbox{Gravitational acceleration}\\
h_0&=\mbox{Upstream water level (m).}
\end{align*}


For large values of $\delta_w$ the flow is modeled as a weir by the
equation
\begin{equation}
Q_w(h_0)=C_wB_g\sqrt{2g}h_0^{3/2}
\end{equation}
where
\begin{align*}
C_w&=\mbox{Weir discharge coefficient.}
\end{align*}
The angle of opening, $\delta_w$, for high angles is considered the
angle where the weir skims over the free flow nappe (\cite{Litrico2005}).\\
In another paper published by \cite{Belaud2008}, Vlugter gates were
modeled in submerged flow conditions. Flow through the gate
consisted of flow under the gate and flow around the sides.  These
two flow regimes were modeled separately, where flow under the gate
behaves as flow through and orifice, and the flow around the sides
behaving as flow over a weir \cite{Belaud2008}.  Flow under the gate
is described by the equation
\begin{equation}
Q_u=C_uA_u\sqrt{2gh_0(1-s)}
\end{equation}
where
\begin{align*}
Q_u&=\mbox{Flow under gate}\\
C_u&=\mbox{Contraction coefficient}\\
A_u&=\mbox{Opening area under gate}\\
h_0&=\mbox{Upstream water height}\\
s&=h_2/h_0\mbox{ is the submergence ratio}\\
h_2&=\mbox{Downstream water height.}
\end{align*}

The weir behavior around the sides of the gate are modeled by the
equations
\begin{equation}
Q_w=C_wB_w\sqrt{2g}H_0^{3/2}
\end{equation}
where
\begin{align*}
Q_w&=\mbox{Flow around the sides of the gate}\\
C_w&=\mbox{Weir discharge coefficient}\\
B_w&=\mbox{Weir width}\\
H_0&=\mbox{Upstream head above the weir}
\end{align*}
The weir coefficient, usually around 0.385, can be expressed as a
function of $H_0$ and $L_w$, the weir length by the equation
\begin{equation}
C_w=C_{w_0}\left\{1-frac{2}{9\left(1+(H_0/L_w)^4\right)}\right\}
\end{equation}
where $C_{w_0}$ is a constant discharge coefficient
\cite{Belaud2008}.  The flow is then reduced by a factor submergence
factor. This model was calibrated using laboratory testing of flow
rates and
opening angles, and fit quite well to the measured flow rates.\\
\cite{Burt2001} also modeled flap gate flow and opening angles.
Maximum flow was calculated as an open weir, and partial flow was
modeled as an orifice.

\subsection{Inflow}
Inflow to a waste water treatment plant (WWTP) is a crucial design
criteria.  Under steady state conditions, a WWTP gives satisfactory
performance because these conditions are within design conditions
\cite{El-Din2002}. It is during peak loads that permit incompliances
usually occur, and as such, predicting peak inflows is vitally
important. WWTP inflow is ideally only a function of per capita use.
However, sewage and waste water pipes are usually leaky, resulting
in groundwater and precipitation influence.  Groundwater levels are
related to precipitation, and there is strong correlation between
precipitation and WWTP inflows. \cite{El-Din2002} presented an
artificial neural network (ANN) model to predict inflows to Gold Bar
Wastewater Treatment Plant, a large plant in Alberta, using
precipitation data. Some of the inputs to the ANN were day of the
week, and even hour of the day.  Using the ANN, El-Din and Smith
were able to get a correlation coefficient of more than 0.9 for 7 of
8 rain gauges used, the other gauge being low due to measurement
error.  Using the ANN, \cite{El-Din2002} were able to predict inflow
to about $\pm$ 1 $m^3/s$, where base flow was
around 3.5 $m^3/s$ and peak flows were about 10 to 11 $m^3/s$.\\
A study by \cite{Coulibaly2005} combines three forecasting models to
better improve inflow prediction.  The models used are the Nearest
Neighbor Model (NNM), an ANN, and the conceptual model HSAMI.  A
weighted average was then used to combine each model output.  The
weighted averages always improved forecasting results, but the
relative bias was always positive.  Also, the combined model greatly
increased the reliability of multi day forecasting, with
improvements close to 30\% at four days.  For the Nearest Neighbor
Model, \cite{Coulibaly2005} used four inputs, the two previous days
of river flows, the previous day's precipitation, and the 24 hour
predicted precipitation.  These inputs were then searched against
historical records to obtain the nearest neighbors.  The same inputs
were given to the ANN, and the number of hidden layers was selected
by trial and error.  For the HSAMI model, the inputs are basin area,
maximum and minimum temperature, and precipitation.


\section{Methodology}




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